U.S.-Brazil Cooperative Research: Nielsen Fixed Point Theory and Related Topics

在美国-由国际科学与工程办公室美洲项目资助的巴西合作项目，贝茨的黄将与达西伯格L。费尔南达·贡萨尔维斯Cardona和Lucilia D. Borsari的圣保罗大学的主题在拓扑不动点理论。 主要目的是研究基本群和Nielsen数的计算。 Nielsen不动点理论已经被推广到许多不同的设置，其中包括（i）Nielsen重合理论和（ii）等变Nielsen不动点理论。 拟议的项目试图解决一个更一般的巧合理论，还没有被广泛研究的文献。 本项目将采用障碍理论、群上同调、群论和低维拓扑学等新技术，从而将其与其他主流研究领域联系起来。本项目的成果将对群论、拓扑学和分析产生影响，进而可能应用于解决问题的技术，如偏微分方程。 通过将一名本科生纳入该项目，PI将向一名年轻的数学家介绍一个被认为对本科生来说很难的领域。 本科生是一名女性，巴西的两名数学家是女性。 该项目将促进PI与两个新合作者Borsari和Cardona之间的伙伴关系。

In this U.S.-Brazil collaborative project funded by the Americas Program of the Office of International Science and Engineering, Wong of Bates will collaborate with Daciberg L. Goncalves, Fernanda S. Cardona, and Lucilia D. Borsari of the University of Sao Paulo on topics in topological fixed-point theory. The main objective is to study the fundamental group and the computation of the Nielsen number. Nielsen fixed-point theory has been generalized to many different settings among which are (i) Nielsen coincidence theory and (ii) equivariant Nielsen fixed point theory. The proposed project attempts to tackle a more general coincidence theory that has not been extensively studied in the literature. New techniques from obstruction theory, group cohomology, group theory, and low dimensional topology will be employed, thereby relating it to other mainstream research areas.Results from this project should have impact in group theory, topology and analysis, which in turn may be applied to problem-solving techniques, such as partial differential equations. By incorporating an undergraduate into the project, the PI will introduce a young mathematician to a field that is considered difficult for undergraduates. The undergraduate student is a woman, and two of the mathematicians in Brazil are women. This project will foster partnerships between the PI and two new collaborators, Borsari and Cardona.